I'm looking for a small laptop with a 10.1 to 11.6 inch screen and an x86 or x86-64 CPU that runs GNU/Linux without hardware incompatibility. Are there any good ones?

My current laptop is a Dell Inspiron mini 1012

[…] I use it for hobby programming projects while riding the city bus to and from my day job.

One of my screens got cracked in public transport, so I understand why you prefer smaller devices. Is this your Dell mini 1012?

Such small screen sizes usually only feature a 1366x768 resolution at this time. Even though you are used to 10.1 you may want to look a bit beyond 11.6 and get FHD or better screens in return.

Comparing the 10" Dell mini with my 12.5" ASUS C302C:

270 x 198 x 36 mm
304 x 210 x 13.7 mm

• A Chromebook with Chrome OS cannot run most of these applications. As far as I can tell, they would need to be rewritten from scratch in JavaScript as Chrome apps.

We might need to reevaluate this list from time to time. The move to Android apps solved some problems but I'm not saying that it solves yours. Containers on Chrome OS aka Crostini though may solve your problem, but it's not clear at the moment if it takes one update cycle (6 weeks), more than a few months or if it happens this year at all judging by how it went with Android apps on Chrome OS.

A Chromebook with Crouton begs the user to press space to reenable OS verification (which wipes the drive) every time it turns on. I'm told tools by John Lewis can remove this verification warning from the bootloader, but I assume they void the manufacturer's warranty, and I've had to use my current laptop's warranty before on a loose power jack.

1. Yes you can remove the warning. I would recommend mrchromebox.tech's script though as it is actively maintained. To disable write-protect you'll usually find a DIP switch or a screw that shorts a circuit. If your laptop is still booting you can always recover through recovery media or through the script and revert back to the state where your device is eligible for warranty.
2. In times of USB type-C make sure to get a device with more than one USB-C PD capable port, that should solve this problem. I've heard about loose power jacks, but it didn't happen to me.

Chrome OS Weekly Buying Advice Thread

VictoryGoth posts weekly advice on reddit, at the moment the following devices would meet your criteria, be sure to check that the processor is not an ARM one though:

• Acer Chromebook Spin 11 (11.65" x 8.11" x 0.82"): https://www.acer.com/ac/en/US/content/series-features/acerchromebookspin11
• Asus Chromebook C202SA (307 x 199 x 20.9 mm): https://www.asus.com/Commercial-Laptops/ASUS-Chromebook-Flip-C213NA/specifications/
• HP Chromebook 11 G6 (12.04 x 8.18 x 0.71 in | 306 x 208 x 18.05 mm): http://www8.hp.com/us/en/products/laptops/product-detail.html?oid=18280450#!tab=specs
• Acer Chromebook 11 N7 (11.72" x 8.27" x 0.87"): https://www.acer.com/ac/en/US/content/professional-series-features/acerchromebook11n7
• Acer Chromebook 11 C771 (11.72" x 8.23" x 0.82"): https://www.acer.com/ac/en/US/content/model/NX.GNZAA.002
• Acer Chromebook 11 CB3-132 (11.57" x 8.03" x 0.73"): https://www.acer.com/ac/en/US/content/model/NX.G4XAA.001

As I said, I would check 12.5" models too should you go with a Chromebook, you get higher resolutions and better processors.